X-rays, which are an example of radiation rays, are used in imaging methods in areas of industry, such as non-destructive inspection of the inside of materials, in areas of medical images, such as X-ray photography and X-ray computed tomography (CT), and in other areas. Examples of imaging methods employing X-rays include an absorption contrast method and a phase contrast method.
In the absorption contrast method, an image of a detected object can be obtained by producing an absorption contrast on the basis of the attenuation in X-rays caused when the X-rays pass through the detected object.
Meanwhile, in the phase contrast method, an image of a detected object can be obtained by producing a phase contrast on the basis of a phase change caused when X-rays pass through the detected object. This technique is called X-ray phase imaging. Since X-ray phase imaging achieves an excellent sensitivity with respect to biological soft tissues composed of light elements, application to medical images has been expected.
In the process of analysis, information on a phase change obtained by X-ray phase imaging is wrapped into the range of 2π. Thus, it is necessary to obtain the true phase by unwrapping the wrapped phase to acquire a reconstructed phase image. However, since the phase changes greatly in an edge portion of a detected object, information on the wrapped phase includes a phase jump, that is, a portion in which the phase changes discontinuously. When phase information including such a portion in which the phase changes discontinuously is unwrapped, a problem may occur in which an inconsistency occurs between the portion in which the phase changes discontinuously and a portion in which the phase changes continuously and thus distortion which originally does not exist appears.
Under the circumstances described above, a method for performing unwrapping by carrying out iterative calculations using a least-squares method is disclosed in Non-Patent Citation 1. A method for performing a least-squares method using a weighting function in order to minimize distortion even in a case where a portion in which the phase changes discontinuously exists is also disclosed in Non-Patent Citation 1. The “weighting function” is a function for giving, when unwrapping is performed, different weights to a portion in which the phase changes discontinuously and a portion in which the phase changes continuously. With the use of a weighting function, an image having less distortion can be obtained.
A specific unwrapping method disclosed in Non-Patent Citation 1 is performed as follows:
(i) Wrapped phase information is obtained.
(ii) A tentative true phase value is determined and a weighting function is set on the basis of the determined true phase value.
(iii) An optimal true phase value (first value) is calculated using a least-squares method on the basis of the weighting function set in (ii). That is, the true phase value that is obtained when the sum of squares of residuals is minimum is calculated.
(iv) The weighting function is reset on the basis of the optimal true phase value (first value) calculated in (iii).
(v) An optimal true phase value (second value) is calculated using the least-squares method on the basis of the weighting function set in (iv).
(vi) A more accurate weighting function is obtained and a more accurate true phase value is calculated by performing the above-mentioned calculations repeatedly until the sum of squares of residuals converges to a certain value.
The calculation method described above has a problem in that since iterative calculations are performed while a weighting function and a true phase value are corrected alternately, a long time is required for obtaining an accurate true phase value.
In contrast, when the number of iterative calculations decreases, a weighting function can be obtained quickly and the true phase value can thus be obtained quickly. However, it is difficult to obtain an accurate weighting function and an accurate true phase value.